Secondary Instabilities Form a Codimension-2 Point Accompanied by a Homoclinic Bifurcation

A study of secondary instabilities in ac-driven electroconvection of a planarly aligned nematic liquid crystal is presented. At low frequencies one has a transition from normal rolls to a zigzag pattern and at high frequencies a direct transition from normal to abnormal rolls. The crossover defines a codimension-2 point. This point is also the origin of a line of homoclinic bifurcations, which enable the transition from zigzags to abnormal rolls at lower frequencies.